Trilateration using 4 fixed points
I am trying to figure out a problem where you pretend you're a GPS unit at an unknown target location (latitude and longitude co-ordinates). I was given the data of 4 satellites (latitude and longitude co-ordinate pairs and for each pair a distance in kilometers to the target location and Delta Time). Does anyone know how to calculate the co-ordinates of the target location? I tried doing research but the math involved is way beyond me. Thanking you in advance for any help.
Here is the data:
Satellite 1
LAT 24.54653
LONG -81.79745
HEIGHT (m) 20183000
DELTATIME (s) 0.070808428
Satellite 2
LAT 63.75088
LONG -68.56082
HEIGHT (m) 20183000
DELTATIME (s) 0.069105305
Satellite 3
LAT 53.90460
LONG -166.52657
HEIGHT (m) 20183000
DELTATIME (s) 0.073341842
Satellite 4
LAT 43.41038
LONG -65.61692
HEIGHT (m) 20183000
DELTATIME (s) 0.069680227
Convert your sattelite data from their geographic coordinate system (using lat/long/height) to x/y/z, then solve the navigation equations. If you like, convert the result back to geographic coordinates. If you want to the result to be reasonably accurate, you should figure out the geodetic datum underlying your geographic coordinate system.
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